Question: Simplify the following expression: $z = \dfrac{64r + 16}{-72r + 24}$ You can assume $r \neq 0$.
Explanation: Find the greatest common factor of the numerator and denominator. The numerator can be factored: $64r + 16 = (2\cdot2\cdot2\cdot2\cdot2\cdot2 \cdot r) + (2\cdot2\cdot2\cdot2)$ The denominator can be factored: $-72r + 24 = - (2\cdot2\cdot2\cdot3\cdot3 \cdot r) + (2\cdot2\cdot2\cdot3)$ The greatest common factor of all the terms is $8$ Factoring out $8$ gives us: $z = \dfrac{(8)(8r + 2)}{(8)(-9r + 3)}$ Dividing both the numerator and denominator by $8$ gives: $z = \dfrac{8r + 2}{-9r + 3}$